退化维数下具有“厚度”的仿射刚体的经典模型
Classical models of affinely-rigid bodies with "thickness" in degenerate dimension
摘要：
特别感兴趣的是致力于这种情况下，当我们的对象与仿射自由度的物质空间通常比物理空间的维数低。换句话说，当我们有$m$维的亲和力，刚体在$n$维的物理空间中运动，$m<n$。本文主要研究了平板体的“厚度”作垂直于二维中心平面的一维振荡时的物理情形$m=2$、$n=3$。对于两个“平坦”维中的各向同性情形，某些特殊解，即静止椭圆，类似于天文物理学和地球物理学中众所周知的平衡椭球图形，例如，在地球形状理论中，得到了。
英文摘要：
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have the $m$-dimensional affinely-rigid body moving in the $n$-dimensional physical space, $m<n$. We mainly concentrate on the physical situation $m=2$, $n=3$ when "thickness" of flat bodies performs one-dimensional oscillations orthogonal to the two-dimensional central plane of the body. For the isotropic case in two "flat" dimensions some special solutions, namely, the stationary ellipses, which are analogous to the ellipsoidal figures of equilibrium well known in astro- and geophysics, e.g., in the theory of the Earth's shape, are obtained.
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